Implementation Details: In the case of implementing Panaromic Stitching sequentially by stitching the panaromic canvas with every new image, a significant reduction in size of stitched images is observed. In order to overcome this challenge, one image is chosen to be the reference image to which other images are stitched. In the implementation below, image 3 is chosen to be the reference and there the homography matrix between each of the other images and image 3 is computed in order to stitch the images. Thus the homography matrices obtained are H13,H23,H43 and H53 where Hij is the matrix used to stitch image i to image j. H13=H12 H23 H43=inverse(H34) H53=inverse(H34 H45)
H12,H23,H34,H45 are computed by stitching imaage 1 to image 2,image 2 to image 3,image 3 to image 4 and image 4 to image 5 respectively.
In order to stitch image 1 to image 2, the sift keypoints and decriptors for each image is computed following which descriptors are used to compute all the matches between image 1 and image 2. The inliers are then extracted using RANSAC and are used to compute the homography matrix which is to be used to stitch image 1 to image 2. Here image 1 is interpolated to a scale of 18 while image 2 is interpolated to a scale of 4.
import numpy as np
import cv2
import matplotlib.pyplot as plt
import numpy.linalg as lin
from skimage.transform import warp
C:\Users\Varshini\anaconda3\lib\site-packages\scipy\__init__.py:146: UserWarning: A NumPy version >=1.16.5 and <1.23.0 is required for this version of SciPy (detected version 1.23.2
warnings.warn(f"A NumPy version >={np_minversion} and <{np_maxversion}"
im1=cv2.imread('im01.jpg')
im2=cv2.imread('im02.jpg')
plt.imshow(im1)
<matplotlib.image.AxesImage at 0x2263d054e50>
plt.imshow(im2)
<matplotlib.image.AxesImage at 0x2263f985850>
Reading image 1 and image 2 and computing SIFT keypoints and descriptors:
im1=plt.imread('im01.jpg')
im1=cv2.resize(im1,(320,240))
img=im1.copy()
sift1 = cv2.SIFT_create()
gray_im1= cv2.cvtColor(im1,cv2.COLOR_BGR2GRAY)
kp1, des1 = sift1.detectAndCompute(im1,None)
img=cv2.drawKeypoints(im1,kp1,img,flags=cv2.DRAW_MATCHES_FLAGS_DRAW_RICH_KEYPOINTS)
im2=plt.imread('im02.jpg')
im2=cv2.resize(im2,(320,240))
img1=im2.copy()
sift2 = cv2.SIFT_create()
gray_im2= cv2.cvtColor(im2,cv2.COLOR_BGR2GRAY)
kp2, des2 = sift2.detectAndCompute(im2,None)
img1=cv2.drawKeypoints(im2,kp2,img1,flags=cv2.DRAW_MATCHES_FLAGS_DRAW_RICH_KEYPOINTS)
plt.imshow(img)
<matplotlib.image.AxesImage at 0x226307110a0>
plt.imshow(img1)
<matplotlib.image.AxesImage at 0x1cf0f698ca0>
des1.shape
(1567, 128)
des2.shape
Obtaining matches for every descriptor:
threshold=1.5
best_match=1
(des1[0,:]-des2[0,:]).shape
(128,)
threshold=1.5
matches=[]
scores=[]
dist=[]
for i in range(0,des1.shape[0]):
#print(i)
closest_distance=1e10
second_closest_dist=1e10
best_match=None
dist_temp=[]
for j in range(0,des2.shape[0]):
d = des1[i,:] - des2[j,:]
squared_dist = np.sum(d**2)
dist_temp.append(squared_dist)
#print(squared_dist)
if squared_dist<closest_distance:
# print(j)
# print(closest_distance)
# print(squared_dist)
second_closest_dist=closest_distance
closest_distance=squared_dist
best_match=j
elif squared_dist<second_closest_dist:
second_closest_dist=squared_dist
if (threshold * closest_distance < second_closest_dist) and (best_match != None):
#print(i)
#print(j)
matches.append([i,best_match])
scores.append(closest_distance)
dist.append(dist_temp)
min(dist[0])
73517.0
matches
[[10, 92], [61, 490], [148, 280], [235, 428], [236, 94], [277, 494], [278, 494], [279, 494], [282, 385], [290, 3], [301, 17], [306, 8], [321, 31], [326, 50], [335, 56], [350, 67], [352, 61], [354, 330], [357, 86], [360, 86], [362, 86], [363, 86], [369, 90], [383, 101], [387, 101], [391, 101], [395, 101], [397, 101], [400, 101], [402, 101], [406, 428], [407, 94], [409, 120], [414, 124], [420, 109], [421, 121], [434, 128], [436, 128], [437, 140], [439, 139], [442, 128], [444, 128], [449, 139], [450, 128], [455, 251], [457, 147], [459, 155], [463, 152], [470, 159], [472, 163], [474, 172], [475, 176], [476, 173], [479, 179], [483, 244], [484, 181], [485, 182], [487, 187], [490, 185], [493, 198], [497, 191], [498, 207], [499, 208], [504, 201], [511, 217], [513, 218], [519, 223], [520, 222], [523, 228], [525, 229], [533, 238], [534, 238], [536, 236], [537, 237], [538, 247], [539, 242], [543, 244], [546, 252], [547, 248], [548, 250], [551, 257], [552, 259], [555, 256], [557, 485], [563, 271], [569, 191], [572, 159], [574, 280], [575, 279], [577, 278], [579, 276], [580, 146], [586, 288], [587, 282], [588, 283], [590, 288], [591, 296], [594, 300], [595, 301], [598, 294], [600, 308], [602, 294], [603, 307], [605, 309], [609, 304], [610, 312], [620, 321], [622, 323], [623, 323], [626, 325], [627, 327], [629, 393], [637, 62], [640, 334], [655, 332], [662, 94], [672, 62], [684, 363], [685, 10], [686, 375], [688, 373], [693, 367]]
matches
[[1585, 678], [1584, 779], [1582, 981], [1581, 656], [1579, 653], [1578, 652], [1567, 688], [1564, 647], [1562, 654], [1558, 655], [1556, 659], [1554, 623], [1549, 625], [1531, 615], [1526, 628], [1521, 583], [1519, 642], [1503, 1137], [1501, 1222], [1492, 981], [1470, 562], [1468, 558], [1466, 574], [1465, 573], [1464, 558], [1459, 556], [1454, 565], [1453, 222], [1451, 222], [1441, 554], [1440, 554], [1435, 552], [1425, 493], [1424, 183], [1422, 183], [1421, 183], [1418, 542], [1412, 529], [1405, 531], [1404, 530], [1403, 532], [1398, 527], [1393, 507], [1391, 516], [1388, 514], [1386, 501], [1385, 515], [1383, 512], [1373, 500], [1371, 483], [1368, 493], [1367, 482], [1366, 494], [1365, 493], [1363, 496], [1362, 495], [1359, 488], [1358, 487], [1356, 484], [1352, 470], [1351, 472], [1349, 474], [1348, 478], [1347, 454], [1345, 333], [1339, 457], [1336, 465], [1334, 452], [1331, 456], [1329, 343], [1328, 459], [1325, 462], [1317, 447], [1316, 446], [1315, 445], [1314, 443], [1304, 434], [1303, 440], [1300, 1137], [1295, 430], [1290, 1147], [1287, 414], [1278, 409], [1277, 408], [1276, 324], [1275, 402], [1272, 399], [1267, 286], [1264, 392], [1261, 390], [1257, 389], [1256, 381], [1252, 380], [1248, 267], [1244, 377], [1243, 376], [1240, 376], [1239, 372], [1234, 357], [1228, 366], [1227, 365], [1225, 333], [1217, 336], [1209, 334], [1207, 354], [1206, 334], [1204, 335], [1203, 348], [1201, 351], [1200, 350], [1196, 326], [1194, 325], [1190, 329], [1189, 321], [1186, 318], [1185, 323], [1182, 788], [1181, 419], [1180, 316], [1171, 311], [1169, 105], [1165, 307], [1163, 309], [1160, 306], [1157, 292], [1156, 296], [1155, 288], [1149, 304], [1147, 301], [1141, 398], [1140, 283], [1119, 377], [1118, 376], [1116, 280], [1112, 257], [1111, 259], [1106, 243], [1102, 236], [1101, 236], [1100, 236], [1098, 236], [1087, 241], [1085, 235], [1074, 199], [1072, 199], [1070, 199], [1068, 199], [1067, 199], [1065, 199], [1064, 203], [1063, 199], [1061, 206], [1060, 205], [1058, 197], [1057, 197], [1056, 197], [1053, 184], [1051, 183], [1050, 183], [1047, 183], [1045, 638], [1041, 159], [1040, 784], [1014, 25], [1009, 143], [1008, 142], [1006, 981], [1003, 1025], [996, 144], [993, 115], [990, 141], [977, 107], [975, 99], [962, 122], [961, 121], [960, 102], [959, 119], [955, 110], [954, 88], [952, 728], [948, 81], [947, 81], [945, 81], [944, 95], [942, 81], [937, 93], [932, 70], [926, 77], [924, 451], [918, 48], [914, 39], [913, 46], [911, 53], [910, 46], [908, 46], [907, 55], [902, 192], [888, 36], [884, 21], [883, 11], [878, 16], [876, 12], [842, 159], [839, 0], [838, 0], [791, 105], [782, 312], [757, 767], [746, 732], [728, 614], [719, 1107], [718, 512], [703, 354], [702, 355], [631, 1138], [583, 779], [557, 105], [556, 1137], [536, 624], [534, 544], [521, 1137], [509, 183], [478, 484], [477, 1209], [474, 1185], [472, 753], [471, 753], [468, 753], [463, 478], [458, 760], [439, 490], [409, 491], [406, 1080], [392, 105], [349, 490], [252, 767], [231, 1065], [186, 656], [185, 34], [173, 855], [161, 488], [151, 676], [71, 16], [50, 526], [47, 487], [39, 753], [36, 753]]
ind=np.argsort(np.array(scores))
matches1=[]
matches_img1=[]
matches_img2=[]
for i in ind:
matches1.append(matches[i])
matches_img1.append(matches[i][0])
matches_img2.append(matches[i][1])
matches1
[[437, 140], [493, 198], [463, 152], [563, 271], [552, 259], [421, 121], [543, 244], [539, 242], [414, 124], [459, 155], [444, 128], [383, 101], [603, 307], [436, 128], [326, 50], [485, 182], [577, 278], [362, 86], [449, 139], [442, 128], [519, 223], [600, 308], [575, 279], [409, 120], [627, 327], [407, 94], [470, 159], [547, 248], [487, 187], [586, 288], [523, 228], [499, 208], [391, 101], [306, 8], [457, 147], [538, 247], [400, 101], [10, 92], [476, 173], [335, 56], [551, 257], [490, 185], [598, 294], [587, 282], [483, 244], [395, 101], [321, 31], [484, 181], [533, 238], [626, 325], [588, 283], [605, 309], [497, 191], [686, 375], [574, 280], [434, 128], [472, 163], [579, 276], [397, 101], [498, 207], [534, 238], [369, 90], [513, 218], [590, 288], [572, 159], [511, 217], [520, 222], [622, 323], [569, 191], [623, 323], [352, 61], [504, 201], [685, 10], [475, 176], [548, 250], [591, 296], [439, 139], [301, 17], [450, 128], [688, 373], [360, 86], [602, 294], [474, 172], [595, 301], [609, 304], [363, 86], [655, 332], [455, 251], [61, 490], [406, 428], [546, 252], [357, 86], [236, 94], [479, 179], [640, 334], [235, 428], [354, 330], [637, 62], [662, 94], [610, 312], [594, 300], [525, 229], [537, 237], [693, 367], [536, 236], [684, 363], [402, 101], [672, 62], [350, 67], [555, 256], [620, 321], [278, 494], [387, 101], [420, 109], [279, 494], [148, 280], [290, 3], [277, 494], [580, 146], [557, 485], [629, 393], [282, 385]]
x1=[]
y1=[]
x2=[]
y2=[]
for i in range(0,len(matches1)):
x1.append(kp1[matches1[i][0]].pt[0])
y1.append(kp1[matches1[i][0]].pt[1])
x2.append(kp2[matches1[i][1]].pt[0]+im2.shape[1])
y2.append(kp2[matches1[i][1]].pt[1])
coordinates_im1=[]
coordinates_im2=[]
for i in range(0,len(matches1)):
coordinates_im1.append([int(kp1[matches1[i][0]].pt[0]),int(kp1[matches1[i][0]].pt[1])])
coordinates_im2.append([int(kp2[matches1[i][1]].pt[0]+im2.shape[1]),int(kp2[matches1[i][1]].pt[1])])
# x1.append(kp1[matches1[i][0]].pt[0])
# y1.append(kp1[matches1[i][0]].pt[1])
# x2.append(kp2[matches1[i][1]].pt[0]+im2.shape[1])
# y2.append(kp2[matches1[i][1]].pt[1])
x2
[370.8848304748535, 397.84622955322266, 374.8287010192871, 424.7959518432617, 421.0082092285156, 364.09968185424805, 414.7709274291992, 414.48877716064453, 364.44944763183594, 375.27701568603516, 368.48412704467773, 356.5718460083008, 433.58336639404297, 368.48412704467773, 340.05978202819824, 391.2531967163086, 427.76734161376953, 349.6298007965088, 370.6371536254883, 368.48412704467773, 404.86832427978516, 433.9596862792969, 428.52069091796875, 363.8125991821289, 443.77030181884766, 355.10396575927734, 376.3925094604492, 417.5693359375, 393.83910369873047, 430.8561096191406, 407.1375503540039, 401.05284881591797, 356.5718460083008, 327.9500107765198, 373.0674591064453, 415.2940979003906, 356.5718460083008, 354.1196746826172, 382.17344665527344, 341.14271354675293, 421.0082092285156, 393.35787200927734, 432.64173126220703, 429.90663146972656, 414.7709274291992, 356.5718460083008, 335.3413677215576, 389.23133850097656, 409.0311508178711, 443.0358428955078, 429.90663146972656, 434.5335388183594, 396.03295135498047, 475.6605529785156, 428.69798278808594, 368.48412704467773, 379.43370819091797, 427.4004898071289, 356.5718460083008, 400.3992614746094, 409.0311508178711, 350.81196784973145, 403.4462356567383, 430.8561096191406, 376.3925094604492, 403.4462356567383, 404.35035705566406, 441.84900665283203, 396.03295135498047, 441.84900665283203, 342.5110092163086, 399.23570251464844, 329.02450942993164, 383.2699165344238, 418.602294921875, 432.71553802490234, 370.6371536254883, 331.0936107635498, 368.48412704467773, 475.5873718261719, 349.6298007965088, 432.64173126220703, 381.72815704345703, 433.00086975097656, 433.0660858154297, 349.6298007965088, 447.5455627441406, 419.95056915283203, 581.4468994140625, 504.301025390625, 420.09120178222656, 349.6298007965088, 355.10396575927734, 386.7981491088867, 449.7522888183594, 504.301025390625, 446.3007278442383, 342.5110092163086, 355.10396575927734, 435.25138092041016, 433.00086975097656, 407.1375503540039, 408.9912338256836, 474.9309997558594, 408.9912338256836, 472.0926208496094, 356.5718460083008, 342.5110092163086, 344.5253086090088, 420.9447937011719, 441.8051300048828, 598.1812438964844, 356.5718460083008, 361.5274353027344, 598.1812438964844, 428.69798278808594, 325.0057134628296, 598.1812438964844, 372.87266540527344, 569.0812530517578, 485.47581481933594, 480.13352966308594]
im_concat = cv2.hconcat([im1, im2])
image=im_concat.copy()
for i in range(0,len(matches1)):
image = cv2.line(im_concat,coordinates_im1[i],coordinates_im2[i],(0, 255, 0),thickness=5)
plt.imshow(image)
<matplotlib.image.AxesImage at 0x22641944f10>
coordinates_im1_hm=[]
coordinates_im2_hm=[]
for i in range(0,len(matches1)):
coordinates_im1_hm.append([int(kp1[matches1[i][0]].pt[0]),int(kp1[matches1[i][0]].pt[1]),1])
coordinates_im2_hm.append([int(kp2[matches1[i][1]].pt[0]),int(kp2[matches1[i][1]].pt[1]),1])
Applying RANSAC to exract inliers from all matches:
import random
#dist=[]
iterations=200
n=5
inliers_max=0
for t in range(0,iterations):
rand_indices=[]
points=[]
coordinates_1=[]
coordinates_2=[]
for i in range(0,5):
rand_index=random.sample(range(0, len(matches1)), 1)
if rand_index not in rand_indices:
rand_indices.append(rand_index)
for k in rand_indices:
coordinates_1.append(np.array(kp1[matches1[k[0]][0]].pt,dtype=int))
coordinates_2.append(np.array(kp2[matches1[k[0]][1]].pt,dtype=int))
coordinates_1_hm=[]
coordinates_2_hm=[]
A = []
b = []
for i in range(len(coordinates_1)):
s_x, s_y = coordinates_1[i]
coordinates_1_hm.append([s_x,s_y,1])
d_x, d_y = coordinates_2[i]
coordinates_2_hm.append([d_x,d_y,1])
A.append([s_x, s_y, 1, 0, 0, 0, -(d_x)*(s_x), -(d_x)*(s_y),-d_x])
A.append([0, 0, 0, s_x, s_y, 1, -(d_y)*(s_x), -(d_y)*(s_y),-d_y])
b += [d_x, d_y]
A = np.array(A)
#h = np.linalg.lstsq(A, b,rcond=-1)[0]
#h = np.concatenate((h, [1]), axis=-1)
import scipy.linalg as linalg
A = np.array(A)
U, Sigma, V_transpose = linalg.svd(A)
H = np.reshape(V_transpose[-1], (3,3))
coordinates_1_transform=np.dot(H,np.array(coordinates_im1_hm).T)
dx=(np.array(coordinates_1_transform)[0]/np.array(coordinates_1_transform)[2])-(np.array(coordinates_im2_hm).T[0]/np.array(coordinates_im2_hm).T[2])
dy=(np.array(coordinates_1_transform)[1]/np.array(coordinates_1_transform)[2])-(np.array(coordinates_im2_hm).T[1]/np.array(coordinates_im2_hm).T[2])
inliers_f=np.array(dx**2+dy**2<3**2,dtype=int)
#dist.append(dx**2+dy**2)
inliers_num = np.sum(inliers_f)
#if inliers_num==5:
#print(dx**2+dy**2)
print(inliers_num)
if inliers_num > inliers_max:
inliers_max = inliers_num
inliers_indices=[index for index in range(len(inliers_f)) if inliers_f[index] ==1]
for inlier_ind in inliers_indices:
inliers_X1 = np.array(coordinates_im1_hm)[inliers_indices]
inliers_X2 = np.array(coordinates_im2_hm)[inliers_indices]
best_X1 = np.array(coordinates_1) # the X1 keypoints that matches best
best_X2 = np.array(coordinates_2) # the X2 keypoints that matches best
best_H12 = H; # the transformation between best X1 and X2
1 18 70 1 0 8 2 2 2 2 12 2 0 0 0 3 0 3 0 3 4 2 1 0 1 1 4 10 2 0 0 0 1 6 0 70 2 3 19 0 5 2 0 3 6 2 5 1 13 3 0 3 1 1 3 5 1 71 0 0 0 0 0 2 0 66 71 4 2 4 51 1 1 58 0 1 6 2 2 0 0 8 1 2 1 3 46 2 8 2 2 1 5 1 70 3 3 2 0 10 2 7 0 4 2 71 6 3 68 0 1 70 8 2 4 15 0 1 0 1 0 36 4 33 0 0 3 2 0 3 8 0 0 1 0 0 1 1 1 0 0 1 2 4 1 5 2 8 2 1 2 3 0 7 1 44 4 3 4 6 0 10 70 6 4 3 2 4 1 5 2 1 10 1 1 3 0 9 22 0 10 11 2 0 2 20 3 2 0 4 1 4 2 4 33 69 8 21 1 1
dist
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len(inliers_X1)
114
coordinates_im1_inliers=[]
coordinates_im2_inliers=[]
for i in range(0,len(inliers_X1)):
coordinates_im1_inliers.append([inliers_X1[i][0],inliers_X1[i][1]])
coordinates_im2_inliers.append([inliers_X2[i][0]+im2.shape[1],inliers_X2[i][1]])
coordinates_im1_inliers=[]
coordinates_im2_inliers=[]
for i in range(0,len(inliers_X1)):
coordinates_im1_inliers.append([inliers_X1[i][0],inliers_X1[i][1]])
coordinates_im2_inliers.append([inliers_X2[i][0]+im2.shape[1],inliers_X2[i][1]])
im_concat = cv2.hconcat([im1, im2])
image=im_concat.copy()
for i in range(0,len(inliers_X1)):
image = cv2.line(im_concat,coordinates_im1_inliers[i],coordinates_im2_inliers[i],(0, 255, 0),thickness=5)
plt.imshow(image)
<matplotlib.image.AxesImage at 0x226486bac70>
len(inliers_X1)
103
Interpolating images and appending scaled coordinates:
im2_interpolate=cv2.resize(im2,(4*im1.shape[1],4*im1.shape[0]),fx=4, fy=4, interpolation=cv2.INTER_CUBIC)
inliers_X1_scaled=[]
inliers_X2_scaled=[]
for i in range(0,len(inliers_X1)):
inliers_X1_scaled.append([18*inliers_X1[i][0],18*inliers_X1[i][1]])
inliers_X2_scaled.append([4*inliers_X2[i][0],4*inliers_X2[i][1]])
#im1=plt.imread('im01.jpg')
im1_interpolate=cv2.resize(im1,(18*im1.shape[1],18*im1.shape[0]),fx=16, fy=16, interpolation=cv2.INTER_CUBIC)
plt.imshow(im1_interpolate)
<matplotlib.image.AxesImage at 0x22648720520>
# A = []
# b = []
# for i in range(len(inliers_X1)):
# s_x, s_y = inliers_X1_scaled[i][0:2]
# # coordinates_1_hm.append([s_x,s_y,1])
# d_x, d_y = inliers_X2[i][0:2]
# #coordinates_2_hm.append([d_x,d_y,1])
# A.append([s_x, s_y, 1, 0, 0, 0, -(d_x)*(s_x), -(d_x)*(s_y),-d_x])
# A.append([0, 0, 0, s_x, s_y, 1, -(d_y)*(s_x), -(d_y)*(s_y),-d_y])
# b += [d_x, d_y]
# A = np.array(A)
# #h = np.linalg.lstsq(A, b,rcond=-1)[0]
# #h = np.concatenate((h, [1]), axis=-1)
# import scipy.linalg as linalg
# A = np.array(A)
# U, Sigma, V_transpose = linalg.svd(A)
# H = np.reshape(V_transpose[-1], (3,3))
Generating homography matrix using scaled inliers:
A = []
b = []
for i in range(len(inliers_X1)):
s_x, s_y = inliers_X1_scaled[i][0:2]
# coordinates_1_hm.append([s_x,s_y,1])
d_x, d_y = inliers_X2_scaled[i][0:2]
#coordinates_2_hm.append([d_x,d_y,1])
A.append([s_x, s_y, 1, 0, 0, 0, -(d_x)*(s_x), -(d_x)*(s_y),-d_x])
A.append([0, 0, 0, s_x, s_y, 1, -(d_y)*(s_x), -(d_y)*(s_y),-d_y])
b += [d_x, d_y]
A = np.array(A)
#h = np.linalg.lstsq(A, b,rcond=-1)[0]
#h = np.concatenate((h, [1]), axis=-1)
import scipy.linalg as linalg
A = np.array(A)
U, Sigma, V_transpose = linalg.svd(A)
H = np.reshape(V_transpose[-1], (3,3))
H12=H
H
array([[ 8.02134559e-04, -3.16764928e-05, -9.52246571e-01],
[ 1.98182812e-04, 6.65990155e-04, -3.05325056e-01],
[ 6.95639480e-07, -3.13480040e-08, 1.39663902e-03]])
H
array([[ 3.24579024e-03, -1.38128829e-04, -9.59160074e-01],
[ 7.57053613e-04, 2.68324795e-03, -2.82827511e-01],
[ 2.66597151e-06, -1.46999358e-07, 1.49128263e-03]])
#h1,w1=im1_interpolate.shape[0:2]
#plt.imshow(im1_interpolate)
<matplotlib.image.AxesImage at 0x22634b453d0>
Transforming border position coordinates of image 1 to determine canvas size:
h1,w1=im1_interpolate.shape[0:2]
vertex = np.array([[0, 0, 1], [0, h1, 1], [w1, 0, 1], [w1, h1, 1]]);
pos = np.dot(H ,vertex.T); #position of transformed vertices
row=(pos[1,:]/pos[2,:]).astype(int)
col=(pos[0,:]/pos[2,:]).astype(int)
col_min = min(col)
col_max = max(col)
row_min = min(row)
row_max = max(row)
if col_min>0:
col_min=1
if row_min>0:
row_min=1
canvas1 = np.zeros([row_max-row_min+100, col_max-col_min+500, 3])
canvas1.shape
plt.imshow(canvas1)
<matplotlib.image.AxesImage at 0x2263669ce80>
# im2=plt.imread('im02.jpg')
# plt.imshow(im2)
<matplotlib.image.AxesImage at 0x1cf20cd33a0>
Placing interpolated image 2 on the canvas:
for y in range(0,im2_interpolate.shape[0]):
for x in range(0,im2_interpolate.shape[1]):
tx2 = x-col_min
ty2 = y-row_min
if ty2<canvas1.shape[0] and tx2<canvas1.shape[1]:
canvas1[ty2,tx2] = im2_interpolate[y,x]
plt.imshow(canvas1)
Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).
<matplotlib.image.AxesImage at 0x226364c1c10>
plt.imshow(im2/255)
<matplotlib.image.AxesImage at 0x1cf209ebb20>
plt.imshow(canvas1/255)
<matplotlib.image.AxesImage at 0x1ce9bffb7f0>
h1
1920
Transforming image 1 coordinates using homography matrix and placing on canvas:
for y in range(0, h1):
for x in range(0, w1):
pixel = np.array([x,
y,
1])
# Resource_pixel = np.asarray(np.asmatrix(inv_my_homo) * np.asmatrix(pixel))
#Resource_pixel = np.asarray(np.asmatrix(My_Homography_arr) * np.asmatrix(pixel))
Resource_pixel = np.asarray(H * np.asmatrix(pixel).T)
# Coordinate scale
trans_x = Resource_pixel[0][0] / Resource_pixel[2][0]
trans_y = Resource_pixel[1][0] / Resource_pixel[2][0]
# Continue that pixels not matched
# if (trans_x < 0 or trans_y < 0
# or trans_x > f2.shape[0] - 1 or trans_y > f2.shape[1] - 1):
# # if (trans_x < 0 and trans_y < 0
# # and trans_x > f2.shape[0] - 1 and trans_y > f2.shape[1] - 1):
# continue
# divided by two parts with integer & decimal number
tx = int(trans_x) -col_min
ty = int(trans_y) -row_min
a = trans_x - tx
b = trans_y - ty
#if tx<canvas1.shape[0] and ty<canvas1.shape[1]:
canvas1[ty,tx]=im1_interpolate[y,x]
# Bilinear Interpolation
# if ty+1<im1.shape[0] and tx+1<im1.shape[1]:
# canvas1[ty][tx] = ((((1.0 - a) * (1.0 - b)) * im1[ty,tx])
# + ((a * (1.0 - b)) * im1[ty,tx + 1])
# + ((a * b) * im1[ty + 1,tx + 1])
# + (((1.0 - a) * b) * im1[ty + 1,tx]))
# Image stitch
# M, N = f1.shape[:2]
# f_stitched = np.copy(warped)
#f_stitched[0:M, 0:N, :] = f1
# Plot
# plt.subplot(221)
# plt.imshow(f1)
# plt.axis('off')
# coordinates_2=np.array(coordinates_2)
# coordinates_1=np.array(coordinates_1)
# plt.scatter(coordinates_2[:, 0], coordinates_2[:, 1], marker='x')
# plt.subplot(222)
# plt.imshow(f2)
# plt.axis('off')
# plt.scatter(coordinates_1[:, 0], coordinates_1[:, 1], marker='x')
# plt.subplot(223)
plt.imshow(canvas1)
plt.axis('off')
#plt.subplot(224)
#plt.imshow(f_stitched)
#plt.axis('off')
plt.show()
Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).
plt.imshow(canvas1/255)
<matplotlib.image.AxesImage at 0x2263657ed90>
In order to stitch image 2 to image 3, the sift keypoints and decriptors for each image is computed following which descriptors are used to compute all the matches between image 2 and image 3. The inliers are then extracted using RANSAC and are used to compute the homography matrix which is to be used to stitch image 2 to image . Here image 2 is interpolated to a scale of 4 while scale of image 3 remains the same.
Reading image 2 and image 3 and computing their corresponding SIFT keypoints and descriptors:
im1=plt.imread('im02.jpg')
im1=cv2.resize(im1,(320,240))
img=im1.copy()
sift1 = cv2.SIFT_create()
#gray_im1= cv2.cvtColor(im1,cv2.COLOR_BGR2GRAY)
kp1, des1 = sift1.detectAndCompute(im1,None)
img=cv2.drawKeypoints(im1,kp1,img,flags=cv2.DRAW_MATCHES_FLAGS_DRAW_RICH_KEYPOINTS)
im2=plt.imread('im03.jpg')
im2=cv2.resize(im2,(320,240))
img1=im2.copy()
sift2 = cv2.SIFT_create()
gray_im2= cv2.cvtColor(im2,cv2.COLOR_BGR2GRAY)
kp2, des2 = sift2.detectAndCompute(im2,None)
img1=cv2.drawKeypoints(im2,kp2,img1,flags=cv2.DRAW_MATCHES_FLAGS_DRAW_RICH_KEYPOINTS)
Obtaining all matches for each descriptor of image 2 and 3.
threshold=1.5
matches=[]
scores=[]
dist=[]
for i in range(0,des1.shape[0]):
#print(i)
closest_distance=1e10
second_closest_dist=1e10
best_match=None
dist_temp=[]
for j in range(0,des2.shape[0]):
d = des1[i,:] - des2[j,:]
squared_dist = np.sum(d**2)
dist_temp.append(squared_dist)
#print(squared_dist)
if squared_dist<closest_distance:
# print(j)
# print(closest_distance)
# print(squared_dist)
second_closest_dist=closest_distance
closest_distance=squared_dist
best_match=j
elif squared_dist<second_closest_dist:
second_closest_dist=squared_dist
if (threshold * closest_distance < second_closest_dist) and (best_match != None):
#print(i)
#print(j)
matches.append([i,best_match])
scores.append(closest_distance)
dist.append(dist_temp)
ind=np.argsort(np.array(scores))
matches1=[]
matches_img1=[]
matches_img2=[]
for i in ind:
matches1.append(matches[i])
matches_img1.append(matches[i][0])
matches_img2.append(matches[i][1])
matches1
[[400, 172], [413, 189], [399, 168], [398, 171], [516, 295], [467, 253], [415, 190], [375, 142], [490, 274], [325, 91], [401, 169], [430, 214], [244, 14], [423, 201], [492, 276], [357, 130], [479, 264], [505, 287], [464, 248], [431, 216], [443, 228], [374, 141], [261, 31], [323, 89], [372, 143], [468, 254], [441, 227], [472, 255], [480, 265], [456, 241], [466, 252], [403, 178], [427, 218], [473, 258], [500, 284], [363, 134], [386, 153], [341, 110], [520, 300], [342, 108], [519, 298], [338, 107], [302, 64], [447, 233], [303, 65], [295, 61], [518, 302], [324, 82], [428, 208], [293, 66], [368, 140], [370, 140], [344, 93], [453, 238], [440, 229], [279, 44], [465, 251], [512, 296], [496, 279], [487, 270], [404, 174], [497, 281], [391, 160], [339, 105], [498, 283], [460, 245], [265, 41], [354, 128], [308, 68], [463, 250], [350, 125], [469, 249], [349, 123], [306, 62], [343, 111], [434, 223], [504, 286], [315, 80], [365, 133], [359, 129], [275, 48], [439, 230], [322, 88], [337, 106], [319, 84], [271, 36], [282, 52], [277, 43], [313, 71], [268, 38], [454, 239], [307, 69], [273, 21], [371, 138], [336, 107], [290, 55], [369, 138], [283, 53], [432, 217], [311, 75], [247, 13], [376, 146], [406, 175], [527, 306], [396, 164], [345, 94], [289, 54], [353, 122], [248, 18], [395, 163], [250, 20], [478, 262], [317, 79], [316, 78], [437, 225], [327, 92], [294, 67], [503, 289], [360, 127], [320, 81], [455, 240], [424, 202], [301, 60], [521, 301], [425, 203], [270, 35], [410, 296], [280, 49], [446, 232], [408, 177], [409, 181], [310, 63], [355, 119], [335, 106], [402, 167], [535, 323], [347, 115], [195, 38], [502, 285], [274, 47], [377, 148], [321, 83], [230, 0], [238, 23], [538, 324], [346, 99], [312, 74], [281, 42], [486, 228], [166, 23], [348, 117], [474, 256], [373, 145], [68, 195], [388, 156], [491, 275], [262, 31], [389, 158], [334, 103], [133, 69], [524, 305], [523, 300], [495, 217], [328, 90], [135, 69], [436, 222], [407, 180], [239, 23], [242, 12], [95, 106], [278, 47], [251, 19], [534, 322], [364, 134], [381, 137], [481, 264], [383, 147], [152, 47], [129, 69], [414, 185], [421, 247], [264, 16], [304, 69], [540, 325], [188, 38], [190, 38], [245, 419], [299, 70], [515, 297], [252, 24], [380, 150], [101, 69], [121, 89], [352, 112], [236, 202], [122, 88], [65, 97], [132, 75], [539, 383], [155, 47], [145, 47], [254, 26], [34, 74], [138, 69], [150, 47], [333, 34], [142, 47], [331, 165], [225, 101]]
coordinates_im1=[]
coordinates_im2=[]
for i in range(0,len(matches1)):
coordinates_im1.append([int(kp1[matches1[i][0]].pt[0]),int(kp1[matches1[i][0]].pt[1])])
coordinates_im2.append([int(kp2[matches1[i][1]].pt[0]+im2.shape[1]),int(kp2[matches1[i][1]].pt[1])])
im2.shape
(240, 320, 3)
im_concat = cv2.hconcat([im1, im2])
image=im_concat.copy()
for i in range(0,len(matches1)):
image = cv2.line(im_concat,coordinates_im1[i],coordinates_im2[i],(0, 255, 0),thickness=5)
plt.imshow(image)
<matplotlib.image.AxesImage at 0x2263d1169d0>
coordinates_im1_hm=[]
coordinates_im2_hm=[]
for i in range(0,len(matches1)):
coordinates_im1_hm.append([int(kp1[matches1[i][0]].pt[0]),int(kp1[matches1[i][0]].pt[1]),1])
coordinates_im2_hm.append([int(kp2[matches1[i][1]].pt[0]),int(kp2[matches1[i][1]].pt[1]),1])
Extracting inliers through RANSAC:
coordinates_im1_hm=[]
coordinates_im2_hm=[]
for i in range(0,len(matches1)):
coordinates_im1_hm.append([int(kp1[matches1[i][0]].pt[0]),int(kp1[matches1[i][0]].pt[1]),1])
coordinates_im2_hm.append([int(kp2[matches1[i][1]].pt[0]),int(kp2[matches1[i][1]].pt[1]),1])
import random
iterations=200
n=5
inliers_max=0
for t in range(0,iterations):
rand_indices=[]
points=[]
coordinates_1=[]
coordinates_2=[]
for i in range(0,5):
rand_index=random.sample(range(0, len(matches1)), 1)
if rand_index not in rand_indices:
rand_indices.append(rand_index)
for k in rand_indices:
coordinates_1.append(np.array(kp1[matches1[k[0]][0]].pt,dtype=int))
coordinates_2.append(np.array(kp2[matches1[k[0]][1]].pt,dtype=int))
coordinates_1_hm=[]
coordinates_2_hm=[]
A = []
b = []
for i in range(len(coordinates_1)):
s_x, s_y = coordinates_1[i]
coordinates_1_hm.append([s_x,s_y,1])
d_x, d_y = coordinates_2[i]
coordinates_2_hm.append([d_x,d_y,1])
A.append([s_x, s_y, 1, 0, 0, 0, -(d_x)*(s_x), -(d_x)*(s_y),-d_x])
A.append([0, 0, 0, s_x, s_y, 1, -(d_y)*(s_x), -(d_y)*(s_y),-d_y])
b += [d_x, d_y]
A = np.array(A)
#h = np.linalg.lstsq(A, b,rcond=-1)[0]
#h = np.concatenate((h, [1]), axis=-1)
import scipy.linalg as linalg
A = np.array(A)
U, Sigma, V_transpose = linalg.svd(A)
H = np.reshape(V_transpose[-1], (3,3))
coordinates_1_transform=np.dot(H,np.array(coordinates_im1_hm).T)
dx=(np.array(coordinates_1_transform)[0]/np.array(coordinates_1_transform)[2])-(np.array(coordinates_im2_hm).T[0]/np.array(coordinates_im2_hm).T[2])
dy=(np.array(coordinates_1_transform)[1]/np.array(coordinates_1_transform)[2])-(np.array(coordinates_im2_hm).T[1]/np.array(coordinates_im2_hm).T[2])
inliers_f=np.array(dx**2+dy**2<3**2,dtype=int)
inliers_num = np.sum(inliers_f)
#if inliers_num==5:
#print(dx**2+dy**2)
print(inliers_num)
if inliers_num > inliers_max:
inliers_max = inliers_num
inliers_indices=[index for index in range(len(inliers_f)) if inliers_f[index] ==1]
for inlier_ind in inliers_indices:
inliers_X1 = np.array(coordinates_im1_hm)[inliers_indices]
inliers_X2 = np.array(coordinates_im2_hm)[inliers_indices]
best_X1 = np.array(coordinates_1) # the X1 keypoints that matches best
best_X2 = np.array(coordinates_2) # the X2 keypoints that matches best
best_H12 = H; # the transformation between best X1 and X2
2 133 4 120 102 0 0 0 96 10 1 10 3 38 162 1 2 0 4 17 2 3 10 0 158 0 15 128 3 5 5 83 1 3 2 83 7 26 2 159 3 0 1 129 134 0 4 4 0 8 1 14 43 1 0 0 3 2 157 150 2 3 144 136 0 12 2 5 3 132 67 1 4 142 8 128 82 158 102 0 0 1 0 86 116 2 0 8 18 2 0 151 0 105 0 2 122 9 1 27 1 2 119 3 134 0 160 3 1 157 8 3 1 1 8 42 25 13 94 73 127 0 0 2 1 160 0 2 1 160 107 0 1 158 22 79 1 2 0 6 5 3 59 5 23 0 98 0 1 160 130 59 1 14 78 145 149 10 6 157 1 7 149 159 0 102 1 1 5 2 156 2 0 0 4 2 6 64 2 54 2 8 10 0 1 142 2 43 161 88 1 4 99 151 116 4 41 1 136 2
len(inliers_X1)
362
coordinates_im1_inliers=[]
coordinates_im2_inliers=[]
for i in range(0,len(inliers_X1)):
coordinates_im1_inliers.append([inliers_X1[i][0],inliers_X1[i][1]])
coordinates_im2_inliers.append([inliers_X2[i][0]+im2.shape[1],inliers_X2[i][1]])
im_concat = cv2.hconcat([im1, im2])
image=im_concat.copy()
for i in range(0,len(inliers_X1)):
image = cv2.line(im_concat,coordinates_im1_inliers[i],coordinates_im2_inliers[i],(0, 255, 0),thickness=5)
plt.imshow(image)
<matplotlib.image.AxesImage at 0x2263ea7d3a0>
Interpolating image 2 and appending scaled inlier coordinates for computation of homography matrix: Here image 2 is scaled to a size of 4 while size of image 3 remains the same.
im1_interpolate=cv2.resize(im1,(4*im2.shape[1],4*im2.shape[0]),fx=4, fy=4, interpolation=cv2.INTER_CUBIC)
plt.imshow(im1_interpolate)
<matplotlib.image.AxesImage at 0x2263bbebac0>
inliers_X1_scaled=[]
inliers_X2_scaled=[]
for i in range(0,len(inliers_X1)):
inliers_X1_scaled.append([4*inliers_X1[i][0],4*inliers_X1[i][1]])
inliers_X2_scaled.append([4*inliers_X2[i][0],4*inliers_X2[i][1]])
Computing Homography Matrix:
A = []
b = []
for i in range(len(inliers_X1)):
s_x, s_y = inliers_X1_scaled[i][0:2]
# coordinates_1_hm.append([s_x,s_y,1])
d_x, d_y = inliers_X2[i][0:2]
#coordinates_2_hm.append([d_x,d_y,1])
A.append([s_x, s_y, 1, 0, 0, 0, -(d_x)*(s_x), -(d_x)*(s_y),-d_x])
A.append([0, 0, 0, s_x, s_y, 1, -(d_y)*(s_x), -(d_y)*(s_y),-d_y])
b += [d_x, d_y]
A = np.array(A)
#h = np.linalg.lstsq(A, b,rcond=-1)[0]
#h = np.concatenate((h, [1]), axis=-1)
import scipy.linalg as linalg
A = np.array(A)
U, Sigma, V_transpose = linalg.svd(A)
H = np.reshape(V_transpose[-1], (3,3))
H23=H
im1.shape
(480, 640, 3)
h1,w1=im1_interpolate.shape[0:2]
vertex = np.array([[0, 0, 1], [0, h1, 1], [w1, 0, 1], [w1, h1, 1]]);
pos = np.dot(H ,vertex.T); #position of transformed vertices
row=(pos[1,:]/pos[2,:]).astype(int)
col=(pos[0,:]/pos[2,:]).astype(int)
col_min = min(col)
col_max = max(col)
row_min = min(row)
row_max = max(row)
col_min
-268
col_min
row_min
-95
if col_min>1:
col_min=1
if row_min>1:
row_min=1
canvas3 = np.zeros([row_max-row_min+100,col_max-col_min+200, 3])
canvas3.shape
plt.imshow(canvas3)
<matplotlib.image.AxesImage at 0x22637f51130>
for y in range(0,im2.shape[0]):
for x in range(0,im2.shape[1]):
tx2 = x - col_min
ty2 = y -row_min
#if ty2<canvas3.shape[0] and tx2<canvas3.shape[1]:
canvas3[ty2,tx2] = im2[y,x]
plt.imshow(canvas3/255)
<matplotlib.image.AxesImage at 0x226366ca970>
for y in range(0, h1):
for x in range(0, w1):
pixel = np.array([x,
y,
1])
# Resource_pixel = np.asarray(np.asmatrix(inv_my_homo) * np.asmatrix(pixel))
#Resource_pixel = np.asarray(np.asmatrix(My_Homography_arr) * np.asmatrix(pixel))
Resource_pixel = np.asarray(H* np.asmatrix(pixel).T)
# Coordinate scale
trans_x = Resource_pixel[0][0] / Resource_pixel[2][0]
trans_y = Resource_pixel[1][0] / Resource_pixel[2][0]
# Continue that pixels not matched
# if (trans_x < 0 or trans_y < 0
# or trans_x > f2.shape[0] - 1 or trans_y > f2.shape[1] - 1):
# # if (trans_x < 0 and trans_y < 0
# # and trans_x > f2.shape[0] - 1 and trans_y > f2.shape[1] - 1):
# continue
# divided by two parts with integer & decimal number
tx = int(trans_x) -col_min
ty = int(trans_y) -row_min
a = trans_x - tx
b = trans_y - ty
#if tx<canvas3.shape[0] and ty<canvas3.shape[1]:
canvas3[ty,tx]=im1_interpolate[y,x]
# Bilinear Interpolation
# if ty+1<im1.shape[0] and tx+1<im1.shape[1]:
# canvas1[ty][tx] = ((((1.0 - a) * (1.0 - b)) * im1[ty,tx])
# + ((a * (1.0 - b)) * im1[ty,tx + 1])
# + ((a * b) * im1[ty + 1,tx + 1])
# + (((1.0 - a) * b) * im1[ty + 1,tx]))
# Image stitch
# M, N = f1.shape[:2]
# f_stitched = np.copy(warped)
#f_stitched[0:M, 0:N, :] = f1
# Plot
# plt.subplot(221)
# plt.imshow(f1)
# plt.axis('off')
# coordinates_2=np.array(coordinates_2)
# coordinates_1=np.array(coordinates_1)
# plt.scatter(coordinates_2[:, 0], coordinates_2[:, 1], marker='x')
# plt.subplot(222)
# plt.imshow(f2)
# plt.axis('off')
# plt.scatter(coordinates_1[:, 0], coordinates_1[:, 1], marker='x')
# plt.subplot(223)
plt.imshow(canvas3)
plt.axis('off')
#plt.subplot(224)
#plt.imshow(f_stitched)
#plt.axis('off')
plt.show()
Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).
plt.imshow(im2)
<matplotlib.image.AxesImage at 0x226367b97c0>
Displaying the stitched images:
plt.imshow(canvas3/255)
<matplotlib.image.AxesImage at 0x22638670d60>
In order to stitch image 3 to image 4, the sift keypoints and decriptors for each image is computed following which descriptors are used to compute all the matches between image 2 and image 3. The inliers are then extracted using RANSAC and are used to compute the homography matrix which is to be used to stitch image 2 to image . Here image 4 is interpolated to a scale of 2 while scale of image 3 remains the same.
Reading images 3 and 4 and computing their corresponding SIFT Keypoints and Descriptors respectively:
im1=plt.imread('im03.jpg')
im1=cv2.resize(im1,(320,240))
img=im1.copy()
sift1 = cv2.SIFT_create()
#gray_im1= cv2.cvtColor(im1,cv2.COLOR_BGR2GRAY)
kp1, des1 = sift1.detectAndCompute(im1,None)
img=cv2.drawKeypoints(im1,kp1,img,flags=cv2.DRAW_MATCHES_FLAGS_DRAW_RICH_KEYPOINTS)
im2=plt.imread('im04.jpg')
im2=cv2.resize(im2,(320,240))
img1=im2.copy()
sift2 = cv2.SIFT_create()
gray_im2= cv2.cvtColor(im2,cv2.COLOR_BGR2GRAY)
kp2, des2 = sift2.detectAndCompute(im2,None)
img1=cv2.drawKeypoints(im2,kp2,img1,flags=cv2.DRAW_MATCHES_FLAGS_DRAW_RICH_KEYPOINTS)
Obtaining match for each descriptor in image 3 and 4:
threshold=1.5
matches=[]
scores=[]
dist=[]
for i in range(0,des1.shape[0]):
#print(i)
closest_distance=1e10
second_closest_dist=1e10
best_match=None
dist_temp=[]
for j in range(0,des2.shape[0]):
d = des1[i,:] - des2[j,:]
squared_dist = np.sum(d**2)
dist_temp.append(squared_dist)
#print(squared_dist)
if squared_dist<closest_distance:
# print(j)
# print(closest_distance)
# print(squared_dist)
second_closest_dist=closest_distance
closest_distance=squared_dist
best_match=j
elif squared_dist<second_closest_dist:
second_closest_dist=squared_dist
if (threshold * closest_distance < second_closest_dist) and (best_match != None):
#print(i)
#print(j)
matches.append([i,best_match])
scores.append(closest_distance)
dist.append(dist_temp)
ind=np.argsort(np.array(scores))
matches1=[]
matches_img1=[]
matches_img2=[]
for i in ind:
matches1.append(matches[i])
matches_img1.append(matches[i][0])
matches_img2.append(matches[i][1])
matches1
[[479, 134], [473, 129], [399, 54], [400, 56], [505, 151], [432, 91], [427, 90], [496, 145], [492, 143], [490, 140], [531, 172], [477, 130], [426, 89], [428, 81], [401, 57], [463, 123], [500, 148], [373, 25], [466, 126], [443, 99], [375, 27], [508, 157], [431, 88], [511, 160], [371, 23], [445, 104], [422, 76], [398, 56], [501, 151], [465, 124], [472, 127], [467, 125], [386, 34], [518, 167], [497, 149], [499, 153], [405, 63], [502, 150], [403, 60], [469, 122], [411, 160], [447, 109], [521, 165], [442, 98], [437, 95], [417, 285], [388, 40], [347, 2], [424, 77], [516, 161], [504, 147], [520, 163], [367, 22], [451, 111], [487, 138], [396, 46], [453, 113], [446, 105], [495, 91], [433, 92], [369, 23], [519, 162], [478, 133], [522, 166], [461, 119], [430, 85], [509, 158], [456, 118], [425, 78], [444, 103], [486, 99], [354, 14], [389, 39], [491, 142], [357, 15], [481, 134], [407, 65], [498, 152], [365, 20], [429, 83], [538, 175], [489, 140], [385, 21], [402, 48], [406, 51], [530, 172], [526, 169], [350, 11], [440, 100], [523, 163], [438, 97], [391, 43], [244, 90], [454, 114], [441, 99], [351, 12], [61, 278], [439, 127], [262, 45], [236, 77], [464, 124], [230, 90], [349, 10], [381, 31], [353, 6], [177, 90], [261, 45], [200, 273], [132, 5], [116, 60], [387, 41], [383, 24], [171, 90], [35, 5], [235, 90], [26, 5], [21, 5], [279, 45], [269, 90], [250, 45], [70, 3], [211, 173], [287, 37], [124, 45], [17, 45], [302, 45]]
coordinates_im1=[]
coordinates_im2=[]
for i in range(0,len(matches1)):
coordinates_im1.append([int(kp1[matches1[i][0]].pt[0]),int(kp1[matches1[i][0]].pt[1])])
coordinates_im2.append([int(kp2[matches1[i][1]].pt[0]+im2.shape[1]),int(kp2[matches1[i][1]].pt[1])])
im2.shape
(240, 320, 3)
im_concat = cv2.hconcat([im1, im2])
image=im_concat.copy()
for i in range(0,len(matches1)):
image = cv2.line(im_concat,coordinates_im1[i],coordinates_im2[i],(0, 255, 0),thickness=5)
plt.imshow(image)
<matplotlib.image.AxesImage at 0x2263b2282b0>
coordinates_im1_hm=[]
coordinates_im2_hm=[]
for i in range(0,len(matches1)):
coordinates_im1_hm.append([int(kp1[matches1[i][0]].pt[0]),int(kp1[matches1[i][0]].pt[1]),1])
coordinates_im2_hm.append([int(kp2[matches1[i][1]].pt[0]),int(kp2[matches1[i][1]].pt[1]),1])
Applying RANSAC to obtain the inliers:
coordinates_im1_hm=[]
coordinates_im2_hm=[]
for i in range(0,len(matches1)):
coordinates_im1_hm.append([int(kp1[matches1[i][0]].pt[0]),int(kp1[matches1[i][0]].pt[1]),1])
coordinates_im2_hm.append([int(kp2[matches1[i][1]].pt[0]),int(kp2[matches1[i][1]].pt[1]),1])
import random
iterations=200
n=5
inliers_max=0
for t in range(0,iterations):
rand_indices=[]
points=[]
coordinates_1=[]
coordinates_2=[]
for i in range(0,5):
rand_index=random.sample(range(0, len(matches1)), 1)
if rand_index not in rand_indices:
rand_indices.append(rand_index)
for k in rand_indices:
coordinates_1.append(np.array(kp1[matches1[k[0]][0]].pt,dtype=int))
coordinates_2.append(np.array(kp2[matches1[k[0]][1]].pt,dtype=int))
coordinates_1_hm=[]
coordinates_2_hm=[]
A = []
b = []
for i in range(len(coordinates_1)):
s_x, s_y = coordinates_1[i]
coordinates_1_hm.append([s_x,s_y,1])
d_x, d_y = coordinates_2[i]
coordinates_2_hm.append([d_x,d_y,1])
A.append([s_x, s_y, 1, 0, 0, 0, -(d_x)*(s_x), -(d_x)*(s_y),-d_x])
A.append([0, 0, 0, s_x, s_y, 1, -(d_y)*(s_x), -(d_y)*(s_y),-d_y])
b += [d_x, d_y]
A = np.array(A)
#h = np.linalg.lstsq(A, b,rcond=-1)[0]
#h = np.concatenate((h, [1]), axis=-1)
import scipy.linalg as linalg
A = np.array(A)
U, Sigma, V_transpose = linalg.svd(A)
H = np.reshape(V_transpose[-1], (3,3))
coordinates_1_transform=np.dot(H,np.array(coordinates_im1_hm).T)
dx=(np.array(coordinates_1_transform)[0]/np.array(coordinates_1_transform)[2])-(np.array(coordinates_im2_hm).T[0]/np.array(coordinates_im2_hm).T[2])
dy=(np.array(coordinates_1_transform)[1]/np.array(coordinates_1_transform)[2])-(np.array(coordinates_im2_hm).T[1]/np.array(coordinates_im2_hm).T[2])
inliers_f=np.array(dx**2+dy**2<3**2,dtype=int)
inliers_num = np.sum(inliers_f)
#if inliers_num==5:
#print(dx**2+dy**2)
print(inliers_num)
if inliers_num > inliers_max:
inliers_max = inliers_num
inliers_indices=[index for index in range(len(inliers_f)) if inliers_f[index] ==1]
for inlier_ind in inliers_indices:
inliers_X1 = np.array(coordinates_im1_hm)[inliers_indices]
inliers_X2 = np.array(coordinates_im2_hm)[inliers_indices]
best_X1 = np.array(coordinates_1) # the X1 keypoints that matches best
best_X2 = np.array(coordinates_2) # the X2 keypoints that matches best
best_H12 = H; # the transformation between best X1 and X2
1 0 3 44 0 1 53 3 7 25 6 0 27 6 4 0 81 6 34 5 1 7 3 1 71 0 0 1 3 0 13 1 57 2 4 71 13 0 59 1 2 25 5 6 0 10 6 41 0 0 6 2 1 67 78 3 1 1 0 8 70 77 30 8 79 4 28 1 0 1 5 0 83 6 5 10 6 1 6 1 0 14 6 1 4 0 3 0 8 1 0 10 1 4 1 6 2 1 0 2 3 79 0 0 0 3 0 2 2 11 75 10 1 0 0 2 0 3 1 0 14 83 1 0 17 2 7 1 3 78 37 2 14 0 1 50 4 1 47 29 5 75 4 20 3 0 1 7 68 9 5 0 0 4 27 0 0 0 0 7 25 0 0 3 41 6 38 63 2 34 48 74 4 0 3 5 1 2 5 2 4 46 1 6 31 0 2 2 0 2 2 1 0 3 2 4 8 0 43 2
len(inliers_X1)
363
coordinates_im1_inliers=[]
coordinates_im2_inliers=[]
for i in range(0,len(inliers_X1)):
coordinates_im1_inliers.append([inliers_X1[i][0],inliers_X1[i][1]])
coordinates_im2_inliers.append([inliers_X2[i][0]+im2.shape[1],inliers_X2[i][1]])
im_concat = cv2.hconcat([im1, im2])
image=im_concat.copy()
for i in range(0,len(inliers_X1)):
image = cv2.line(im_concat,coordinates_im1_inliers[i],coordinates_im2_inliers[i],(0, 255, 0),thickness=5)
plt.imshow(image)
<matplotlib.image.AxesImage at 0x2263b0eaee0>
Interpolating image 4 by scale 2 and appending the corresponding scaled inlier coordinates:
inliers_X1_scaled=[]
inliers_X2_scaled=[]
for i in range(0,len(inliers_X1)):
inliers_X1_scaled.append([2*inliers_X1[i][0],2*inliers_X1[i][1]])
inliers_X2_scaled.append([2*inliers_X2[i][0],2*inliers_X2[i][1]])
im2_interpolate=cv2.resize(im2,(2*im2.shape[1],2*im2.shape[0]),fx=2, fy=2, interpolation=cv2.INTER_CUBIC)
plt.imshow(im2_interpolate)
<matplotlib.image.AxesImage at 0x22637cf45b0>
Computing homography matrix using original inliers obtained for image 2 and scaled inlier coordinates obtained for image 4:
A = []
b = []
for i in range(len(inliers_X1)):
s_x, s_y = inliers_X1[i][0:2]
# coordinates_1_hm.append([s_x,s_y,1])
d_x, d_y = inliers_X2_scaled[i][0:2]
#coordinates_2_hm.append([d_x,d_y,1])
A.append([s_x, s_y, 1, 0, 0, 0, -(d_x)*(s_x), -(d_x)*(s_y),-d_x])
A.append([0, 0, 0, s_x, s_y, 1, -(d_y)*(s_x), -(d_y)*(s_y),-d_y])
b += [d_x, d_y]
A = np.array(A)
#h = np.linalg.lstsq(A, b,rcond=-1)[0]
#h = np.concatenate((h, [1]), axis=-1)
import scipy.linalg as linalg
A = np.array(A)
U, Sigma, V_transpose = linalg.svd(A)
H = np.reshape(V_transpose[-1], (3,3))
H_inv=linalg.inv(H)
H34=H
Defining canvas to stitch images 3 and 4:
h1,w1=im1.shape[0:2]
vertex = np.array([[0, 0, 1], [0, h1, 1], [w1, 0, 1], [w1, h1, 1]]);
pos = np.dot(H ,vertex.T); #position of transformed vertices
row=(pos[1,:]/pos[2,:]).astype(int)
col=(pos[0,:]/pos[2,:]).astype(int)
col_min = min(col)
col_max = max(col)
row_min = min(row)
row_max = max(row)
if col_min>1:
col_min=1
if row_min>1:
row_min=1
canvas3 = np.zeros([row_max-row_min+500,col_max-col_min+500, 3])
canvas3.shape
plt.imshow(canvas3)
<matplotlib.image.AxesImage at 0x2263b3f3280>
Placing image 4 onto the canvas:
for y in range(0,im2_interpolate.shape[0]):
for x in range(0,im2_interpolate.shape[1]):
tx2 = x - col_min
ty2 = y -row_min
#if ty2<canvas3.shape[0] and tx2<canvas3.shape[1]:
canvas3[ty2,tx2] = im2_interpolate[y,x]
plt.imshow(canvas3/255)
<matplotlib.image.AxesImage at 0x22635197fd0>
Transforming image 3 coordinates using homography matrix and placing onto canvas:
for y in range(0, h1):
for x in range(0, w1):
pixel = np.array([x,
y,
1])
# Resource_pixel = np.asarray(np.asmatrix(inv_my_homo) * np.asmatrix(pixel))
#Resource_pixel = np.asarray(np.asmatrix(My_Homography_arr) * np.asmatrix(pixel))
Resource_pixel = np.asarray(H* np.asmatrix(pixel).T)
# Coordinate scale
trans_x = Resource_pixel[0][0] / Resource_pixel[2][0]
trans_y = Resource_pixel[1][0] / Resource_pixel[2][0]
# Continue that pixels not matched
# if (trans_x < 0 or trans_y < 0
# or trans_x > f2.shape[0] - 1 or trans_y > f2.shape[1] - 1):
# # if (trans_x < 0 and trans_y < 0
# # and trans_x > f2.shape[0] - 1 and trans_y > f2.shape[1] - 1):
# continue
# divided by two parts with integer & decimal number
tx = int(trans_x) -col_min
ty = int(trans_y) -row_min
a = trans_x - tx
b = trans_y - ty
#if tx<canvas3.shape[0] and ty<canvas3.shape[1]:
canvas3[ty,tx]=im1[y,x]
# Bilinear Interpolation
# if ty+1<im1.shape[0] and tx+1<im1.shape[1]:
# canvas1[ty][tx] = ((((1.0 - a) * (1.0 - b)) * im1[ty,tx])
# + ((a * (1.0 - b)) * im1[ty,tx + 1])
# + ((a * b) * im1[ty + 1,tx + 1])
# + (((1.0 - a) * b) * im1[ty + 1,tx]))
# Image stitch
# M, N = f1.shape[:2]
# f_stitched = np.copy(warped)
#f_stitched[0:M, 0:N, :] = f1
# Plot
# plt.subplot(221)
# plt.imshow(f1)
# plt.axis('off')
# coordinates_2=np.array(coordinates_2)
# coordinates_1=np.array(coordinates_1)
# plt.scatter(coordinates_2[:, 0], coordinates_2[:, 1], marker='x')
# plt.subplot(222)
# plt.imshow(f2)
# plt.axis('off')
# plt.scatter(coordinates_1[:, 0], coordinates_1[:, 1], marker='x')
# plt.subplot(223)
plt.imshow(canvas3)
plt.axis('off')
#plt.subplot(224)
#plt.imshow(f_stitched)
#plt.axis('off')
plt.show()
Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).
plt.imshow(canvas3/255)
<matplotlib.image.AxesImage at 0x2263525d670>
im4=cv2.normalize(canvas3[0:560,0:780]/255, None, 0, 255, cv2.NORM_MINMAX).astype('uint8')
#im4=cv2.resize(im4,(640,480))
#im3.shape
plt.imshow(im4)
<matplotlib.image.AxesImage at 0x2a78744bf40>
In order to stitch image 3 to image 4, the sift keypoints and decriptors for each image is computed following which descriptors are used to compute all the matches between image 2 and image 3. The inliers are then extracted using RANSAC and are used to compute the homography matrix which is to be used to stitch image 2 to image . Here image 4 is interpolated to a scale of 2 while scale of image 3 remains the same.
Reading image 4 and 5 and computing their corresponding SIFT keypoints and descriptors respectively:
im1=plt.imread('im04.jpg')
im1=cv2.resize(im1,(320,240))
# im1=im4.copy()
img=im1.copy()
sift1 = cv2.SIFT_create()
#gray_im1= cv2.cvtColor(im1,cv2.COLOR_BGR2GRAY)
kp1, des1 = sift1.detectAndCompute(im1,None)
img=cv2.drawKeypoints(im1,kp1,img,flags=cv2.DRAW_MATCHES_FLAGS_DRAW_RICH_KEYPOINTS)
im2=plt.imread('im05.jpg')
im2=cv2.resize(im2,(240,320))
#im2=im3.copy()
# im2=im2[0:450,0:600]
#im2=cv2.resize(im2,(640,480))
img1=im2.copy()
sift2 = cv2.SIFT_create()
gray_im2= cv2.cvtColor(im2,cv2.COLOR_BGR2GRAY)
kp2, des2 = sift2.detectAndCompute(im2,None)
img1=cv2.drawKeypoints(im2,kp2,img1,flags=cv2.DRAW_MATCHES_FLAGS_DRAW_RICH_KEYPOINTS)
plt.imshow(im1)
<matplotlib.image.AxesImage at 0x28468b94220>
plt.imshow(im2)
<matplotlib.image.AxesImage at 0x28468bf15b0>
im2.shape
(320, 240, 3)
Obtaining matching descriptor for every descriptor in image 4 and image 5:
threshold=1.5
matches=[]
scores=[]
dist=[]
for i in range(0,des1.shape[0]):
#print(i)
closest_distance=1e10
second_closest_dist=1e10
best_match=None
dist_temp=[]
for j in range(0,des2.shape[0]):
d = des1[i,:] - des2[j,:]
squared_dist = np.sum(d**2)
dist_temp.append(squared_dist)
#print(squared_dist)
if squared_dist<closest_distance:
# print(j)
# print(closest_distance)
# print(squared_dist)
second_closest_dist=closest_distance
closest_distance=squared_dist
best_match=j
elif squared_dist<second_closest_dist:
second_closest_dist=squared_dist
if (threshold * closest_distance < second_closest_dist) and (best_match != None):
#print(i)
#print(j)
matches.append([i,best_match])
scores.append(closest_distance)
dist.append(dist_temp)
ind=np.argsort(np.array(scores))
matches1=[]
matches_img1=[]
matches_img2=[]
for i in ind:
matches1.append(matches[i])
matches_img1.append(matches[i][0])
matches_img2.append(matches[i][1])
matches1
[[151, 60], [196, 184], [169, 97], [198, 186], [183, 147], [247, 292], [197, 185], [176, 133], [200, 188], [204, 200], [167, 82], [76, 112], [207, 202], [172, 107], [237, 275], [164, 78], [245, 288], [215, 221], [170, 99], [185, 167], [230, 262], [285, 397], [187, 166], [161, 68], [147, 59], [150, 61], [279, 342], [208, 216], [190, 174], [223, 60], [162, 70], [178, 149], [206, 201], [240, 281], [158, 65], [92, 313], [191, 177], [220, 235], [181, 148], [272, 324], [42, 321], [118, 84], [166, 83], [131, 8], [99, 7], [281, 129], [110, 181], [278, 47], [78, 396], [211, 219], [141, 40], [174, 106], [201, 189], [37, 107], [221, 270], [269, 255], [205, 203], [13, 86], [243, 286], [77, 395], [49, 359], [186, 165], [236, 282], [105, 79], [132, 86], [51, 178], [16, 86]]
coordinates_im1=[]
coordinates_im2=[]
for i in range(0,len(matches1)):
coordinates_im1.append([int(kp1[matches1[i][0]].pt[0]),int(kp1[matches1[i][0]].pt[1])])
coordinates_im2.append([int(kp2[matches1[i][1]].pt[0]+im2.shape[1]),int(kp2[matches1[i][1]].pt[1])])
im2.shape
(320, 240, 3)
im_concat = cv2.hconcat([im1, cv2.resize(im2,(320,240))])
image=im_concat.copy()
for i in range(0,len(matches1)):
image = cv2.line(im_concat,coordinates_im1[i],coordinates_im2[i],(0, 255, 0),thickness=5)
plt.imshow(image)
<matplotlib.image.AxesImage at 0x28469381bb0>
coordinates_im1_hm=[]
coordinates_im2_hm=[]
for i in range(0,len(matches1)):
coordinates_im1_hm.append([int(kp1[matches1[i][0]].pt[0]),int(kp1[matches1[i][0]].pt[1]),1])
coordinates_im2_hm.append([int(kp2[matches1[i][1]].pt[0]),int(kp2[matches1[i][1]].pt[1]),1])
Obtaining inliers using RANSAC:
coordinates_im1_hm=[]
coordinates_im2_hm=[]
for i in range(0,len(matches1)):
coordinates_im1_hm.append([int(kp1[matches1[i][0]].pt[0]),int(kp1[matches1[i][0]].pt[1]),1])
coordinates_im2_hm.append([int(kp2[matches1[i][1]].pt[0]),int(kp2[matches1[i][1]].pt[1]),1])
import random
iterations=200
n=5
inliers_max=0
for t in range(0,iterations):
rand_indices=[]
points=[]
coordinates_1=[]
coordinates_2=[]
for i in range(0,5):
rand_index=random.sample(range(0, len(matches1)), 1)
if rand_index not in rand_indices:
rand_indices.append(rand_index)
for k in rand_indices:
coordinates_1.append(np.array(kp1[matches1[k[0]][0]].pt,dtype=int))
coordinates_2.append(np.array(kp2[matches1[k[0]][1]].pt,dtype=int))
coordinates_1_hm=[]
coordinates_2_hm=[]
A = []
b = []
for i in range(len(coordinates_1)):
s_x, s_y = coordinates_1[i]
coordinates_1_hm.append([s_x,s_y,1])
d_x, d_y = coordinates_2[i]
coordinates_2_hm.append([d_x,d_y,1])
A.append([s_x, s_y, 1, 0, 0, 0, -(d_x)*(s_x), -(d_x)*(s_y),-d_x])
A.append([0, 0, 0, s_x, s_y, 1, -(d_y)*(s_x), -(d_y)*(s_y),-d_y])
b += [d_x, d_y]
A = np.array(A)
#h = np.linalg.lstsq(A, b,rcond=-1)[0]
#h = np.concatenate((h, [1]), axis=-1)
import scipy.linalg as linalg
A = np.array(A)
U, Sigma, V_transpose = linalg.svd(A)
H = np.reshape(V_transpose[-1], (3,3))
coordinates_1_transform=np.dot(H,np.array(coordinates_im1_hm).T)
dx=(np.array(coordinates_1_transform)[0]/np.array(coordinates_1_transform)[2])-(np.array(coordinates_im2_hm).T[0]/np.array(coordinates_im2_hm).T[2])
dy=(np.array(coordinates_1_transform)[1]/np.array(coordinates_1_transform)[2])-(np.array(coordinates_im2_hm).T[1]/np.array(coordinates_im2_hm).T[2])
inliers_f=np.array(dx**2+dy**2<3**2,dtype=int)
inliers_num = np.sum(inliers_f)
#if inliers_num==5:
#print(dx**2+dy**2)
print(inliers_num)
if inliers_num > inliers_max:
inliers_max = inliers_num
inliers_indices=[index for index in range(len(inliers_f)) if inliers_f[index] ==1]
for inlier_ind in inliers_indices:
inliers_X1 = np.array(coordinates_im1_hm)[inliers_indices]
inliers_X2 = np.array(coordinates_im2_hm)[inliers_indices]
best_X1 = np.array(coordinates_1) # the X1 keypoints that matches best
best_X2 = np.array(coordinates_2) # the X2 keypoints that matches best
best_H12 = H; # the transformation between best X1 and X2
0 0 2 4 2 0 5 0 1 0 2 30 0 0 0 2 1 1 40 0 0 35 3 25 7 3 2 4 7 5 6 8 0 2 1 38 0 4 7 1 8 23 1 1 0 2 1 0 1 0 5 4 39 2 0 1 4 1 1 41 1 2 0 0 5 1 1 2 38 3 0 17 8 14 4 3 10 6 0 1 6 0 40 4 0 11 1 7 2 1 3 1 7 1 4 27 2 2 3 0 6 10 2 3 1 7 7 4 4 5 13 1 9 3 3 0 6 33 1 40 2 0 7 20 1 14 5 5 6 38 5 20 1 1 1 2 0 1 4 25 2 2 0 22 6 4 6 2 0 0 3 10 5 5 2 6 0 2 0 0 0 1 1 5 5 1 0 5 4 2 3 1 2 0 2 3 3 0 0 40 3 2 2 1 8 1 3 2 2 22 4 5 1 12 13 0 4 1 1 1
len(inliers_X1)
41
coordinates_im1_inliers=[]
coordinates_im2_inliers=[]
for i in range(0,len(inliers_X1)):
coordinates_im1_inliers.append([inliers_X1[i][0],inliers_X1[i][1]])
coordinates_im2_inliers.append([inliers_X2[i][0]+im2.shape[1],inliers_X2[i][1]])
im_concat = cv2.hconcat([im1, cv2.resize(im2,(320,240))])
image=im_concat.copy()
for i in range(0,len(inliers_X1)):
image = cv2.line(im_concat,coordinates_im1_inliers[i],coordinates_im2_inliers[i],(0, 255, 0),thickness=5)
plt.imshow(image)
<matplotlib.image.AxesImage at 0x28468d4b250>
Interpolating and scaling image 4 by factor of 2 and image 5 by factor of 5 and appending their scaled inlier coordinates accordingly:
im1_interpolate=cv2.resize(im1,(2*im1.shape[1],2*im1.shape[0]),fx=2, fy=2, interpolation=cv2.INTER_CUBIC)
plt.imshow(im1_interpolate)
<matplotlib.image.AxesImage at 0x28468da0a00>
im2_interpolate=cv2.resize(im2,(4*im2.shape[1],4*im2.shape[0]),fx=4, fy=4, interpolation=cv2.INTER_CUBIC)
plt.imshow(im2_interpolate)
<matplotlib.image.AxesImage at 0x28468e00cd0>
inliers_X1_scaled=[]
inliers_X2_scaled=[]
for i in range(0,len(inliers_X1)):
inliers_X1_scaled.append([2*inliers_X1[i][0],2*inliers_X1[i][1]])
inliers_X2_scaled.append([4*inliers_X2[i][0],4*inliers_X2[i][1]])
Computing the homography matrix:
A = []
b = []
for i in range(len(inliers_X1)):
s_x, s_y = inliers_X1_scaled[i][0:2]
# coordinates_1_hm.append([s_x,s_y,1])
d_x, d_y = inliers_X2_scaled[i][0:2]
#coordinates_2_hm.append([d_x,d_y,1])
A.append([s_x, s_y, 1, 0, 0, 0, -(d_x)*(s_x), -(d_x)*(s_y),-d_x])
A.append([0, 0, 0, s_x, s_y, 1, -(d_y)*(s_x), -(d_y)*(s_y),-d_y])
b += [d_x, d_y]
A = np.array(A)
#h = np.linalg.lstsq(A, b,rcond=-1)[0]
#h = np.concatenate((h, [1]), axis=-1)
import scipy.linalg as linalg
A = np.array(A)
U, Sigma, V_transpose = linalg.svd(A)
H = np.reshape(V_transpose[-1], (3,3))
H_inv=linalg.inv(H)
Defining the canvas size through transformation of border coordinates of image 4:
h1,w1=im1_interpolate.shape[0:2]
vertex = np.array([[0, 0, 1], [0, h1, 1], [w1, 0, 1], [w1, h1, 1]]);
pos = np.dot(H ,vertex.T); #position of transformed vertices
row=(pos[1,:]/pos[2,:]).astype(int)
col=(pos[0,:]/pos[2,:]).astype(int)
col_min = min(col)
col_max = max(col)
row_min = min(row)
row_max = max(row)
H45=H
if col_min>1:
col_min=1
if row_min>1:
row_min=1
canvas3 = np.zeros([row_max-row_min+500, col_max-col_min+500, 3])
canvas3.shape
plt.imshow(canvas3/255)
<matplotlib.image.AxesImage at 0x28468f6aca0>
Placing image 5 onto the canvas:
for y in range(0,im2_interpolate.shape[0]):
for x in range(0,im2_interpolate.shape[1]):
tx2 = x - col_min
ty2 = y -row_min
if ty2<canvas3.shape[0] and tx2<canvas3.shape[1]:
canvas3[ty2,tx2] = im2_interpolate[y,x]
plt.imshow(canvas3/255)
<matplotlib.image.AxesImage at 0x28468fce2e0>
for y in range(0, h1):
for x in range(0, w1):
pixel = np.array([x,
y,
1])
# Resource_pixel = np.asarray(np.asmatrix(inv_my_homo) * np.asmatrix(pixel))
#Resource_pixel = np.asarray(np.asmatrix(My_Homography_arr) * np.asmatrix(pixel))
Resource_pixel = np.asarray(H* np.asmatrix(pixel).T)
# Coordinate scale
trans_x = Resource_pixel[0][0] / Resource_pixel[2][0]
trans_y = Resource_pixel[1][0] / Resource_pixel[2][0]
# Continue that pixels not matched
# if (trans_x < 0 or trans_y < 0
# or trans_x > f2.shape[0] - 1 or trans_y > f2.shape[1] - 1):
# # if (trans_x < 0 and trans_y < 0
# # and trans_x > f2.shape[0] - 1 and trans_y > f2.shape[1] - 1):
# continue
# divided by two parts with integer & decimal number
tx = int(trans_x) -col_min
ty = int(trans_y) -row_min
a = trans_x - tx
b = trans_y - ty
if tx<canvas3.shape[1] and ty<canvas3.shape[0] and tx>0 and ty>0:
canvas3[ty,tx]=im1_interpolate[y,x]
# Bilinear Interpolation
# if ty+1<im1.shape[0] and tx+1<im1.shape[1]:
# canvas1[ty][tx] = ((((1.0 - a) * (1.0 - b)) * im1[ty,tx])
# + ((a * (1.0 - b)) * im1[ty,tx + 1])
# + ((a * b) * im1[ty + 1,tx + 1])
# + (((1.0 - a) * b) * im1[ty + 1,tx]))
# Image stitch
# M, N = f1.shape[:2]
# f_stitched = np.copy(warped)
#f_stitched[0:M, 0:N, :] = f1
# Plot
# plt.subplot(221)
# plt.imshow(f1)
# plt.axis('off')
# coordinates_2=np.array(coordinates_2)
# coordinates_1=np.array(coordinates_1)
# plt.scatter(coordinates_2[:, 0], coordinates_2[:, 1], marker='x')
# plt.subplot(222)
# plt.imshow(f2)
# plt.axis('off')
# plt.scatter(coordinates_1[:, 0], coordinates_1[:, 1], marker='x')
# plt.subplot(223)
plt.imshow(canvas3)
plt.axis('off')
#plt.subplot(224)
#plt.imshow(f_stitched)
#plt.axis('off')
plt.show()
Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).
plt.imshow(canvas3/255)
<matplotlib.image.AxesImage at 0x28470a736a0>
#im2_interpolate.shape
(4800, 6400, 3)
#H23
array([[ 1.28551855e-03, 4.55287041e-05, -9.41988773e-01],
[ 1.25432176e-04, 1.17276050e-03, -3.35621534e-01],
[ 6.04047094e-07, 1.09882888e-07, 3.50592066e-03]])
#H12
array([[ 8.08286449e-04, -3.36354287e-05, -9.56602535e-01],
[ 1.97891855e-04, 6.63078119e-04, -2.91390363e-01],
[ 6.95433494e-07, -5.34618529e-08, 1.45327166e-03]])
#np.matmul(H23,H12)
array([[ 3.92986437e-07, 3.73105853e-08, -2.61196251e-03],
[ 1.00062423e-07, 7.91355813e-07, -9.49469109e-04],
[ 2.94812266e-09, -1.34889459e-10, 4.48520332e-06]])
#np.dot(H23,H12)
array([[ 3.92986437e-07, 3.73105853e-08, -2.61196251e-03],
[ 1.00062423e-07, 7.91355813e-07, -9.49469109e-04],
[ 2.94812266e-09, -1.34889459e-10, 4.48520332e-06]])
#H13
array([[ 1.03906722e-06, -1.53137748e-09, 9.01108849e-01],
[ 2.48220059e-08, 7.77631829e-07, 9.77968807e-02],
[ 4.20074581e-13, -5.87454279e-15, 5.09505512e-06]])
The necessary homography matrices required are computed using those obtained from above. These matrices are then used to stich each image to image 3 i)Image 1 has been interpolated and scaled by a factor of 18 ii)Image 2 has been interpolated and scaled by a factor of 4 iii)Image 3 remains in the same size iv)Image 4 has been interpolated and scaled by a factor of 2 v) Image 5 has been interpolated and scaled by a factor of 4
H13=np.dot(H23,H12)
H43=linalg.inv(H34)
H35 = np.dot(H45 , H34)
H53=linalg.inv(H35)
im1=plt.imread('im01.jpg')
im1=cv2.resize(im1,(320,240))
im1_interpolate=cv2.resize(im1,(18*im1.shape[1],18*im1.shape[0]),fx=18, fy=18, interpolation=cv2.INTER_CUBIC)
h1,w1=im1_interpolate.shape[0:2]
vertex1 = np.array([[0, 0, 1], [0, h1, 1], [w1, 0, 1], [w1, h1, 1]])
im2=plt.imread('im02.jpg')
im2=cv2.resize(im2,(320,240))
im2_interpolate=cv2.resize(im2,(4*im2.shape[1],4*im2.shape[0]),fx=4, fy=4, interpolation=cv2.INTER_CUBIC)
h2,w2=im2_interpolate.shape[0:2]
vertex2 = np.array([[0, 0, 1], [0, h2, 1], [w2, 0, 1], [w2, h2, 1]])
im3=plt.imread('im03.jpg')
im3=cv2.resize(im3,(320,240))
#im3_interpolate=cv2.resize(im3,(4*im3.shape[1],4*im3.shape[0]),fx=4, fy=4, interpolation=cv2.INTER_CUBIC)
h3,w3=im3.shape[0:2]
vertex3 = np.array([[0, 0, 1], [0, h3, 1], [w3, 0, 1], [w3, h3, 1]])
im4=plt.imread('im04.jpg')
im4=cv2.resize(im4,(320,240))
im4_interpolate=cv2.resize(im4,(2*im4.shape[1],2*im4.shape[0]),fx=2, fy=2, interpolation=cv2.INTER_CUBIC)
h4,w4=im4_interpolate.shape[0:2]
vertex4 = np.array([[0, 0, 1], [0, h4, 1], [w4, 0, 1], [w4, h4, 1]])
im5=plt.imread('im05.jpg')
im5=cv2.resize(im5,(240,320))
im5_interpolate=cv2.resize(im5,(4*im5.shape[1],4*im5.shape[0]),fx=4, fy=4, interpolation=cv2.INTER_CUBIC)
h5,w5=im5_interpolate.shape[0:2]
vertex5 = np.array([[0, 0, 1], [0, h5, 1], [w5, 0, 1], [w5, h5, 1]])
Obtaining the canvas size:
In order to determine the canvas size, the transformation coordinates are computed for each image usig their correponding homography matrix. The canvas size is then fixed depending upon the maximum and minimum values of the transformed coordinates for every image.
pos1 = np.dot(H13 ,vertex1.T)
pos2= np.dot(H23 ,vertex2.T)
pos4= np.dot(H43 ,vertex4.T)
pos5= np.dot(H53 ,vertex5.T)
pos=np.hstack([pos1,pos2,pos4,pos5])
pos.shape
(3, 16)
row=(pos[1,:]/pos[2,:]).astype(int)
col=(pos[0,:]/pos[2,:]).astype(int)
col_min = min(col)
col_max = max(col)
row_min = min(row)
row_max = max(row)
row_min
-497
if col_min>1:
col_min=1
if row_min>1:
row_min=1
Defining the canvas
canvas = np.zeros([row_max-row_min+1, col_max-col_min+1, 3])
plt.imshow(canvas/255)
<matplotlib.image.AxesImage at 0x2264143a8b0>
Placing image 3 onto the canvas:
for y in range(0,im3.shape[0]):
for x in range(0,im3.shape[1]):
tx2 = x - col_min
ty2 = y -row_min
if ty2<canvas.shape[0] and tx2<canvas.shape[1]:
canvas[ty2,tx2] = im3[y,x]
plt.imshow(canvas/255)
<matplotlib.image.AxesImage at 0x22641493850>
Stitching every image to canvas: i) Stitching image 1 to canvas using H13:
for y in range(0, h1):
for x in range(0, w1):
pixel = np.array([x,
y,
1])
# Resource_pixel = np.asarray(np.asmatrix(inv_my_homo) * np.asmatrix(pixel))
#Resource_pixel = np.asarray(np.asmatrix(My_Homography_arr) * np.asmatrix(pixel))
Resource_pixel = np.asarray(H13* np.asmatrix(pixel).T)
# Coordinate scale
trans_x = Resource_pixel[0][0] / Resource_pixel[2][0]
trans_y = Resource_pixel[1][0] / Resource_pixel[2][0]
# Continue that pixels not matched
# if (trans_x < 0 or trans_y < 0
# or trans_x > f2.shape[0] - 1 or trans_y > f2.shape[1] - 1):
# # if (trans_x < 0 and trans_y < 0
# # and trans_x > f2.shape[0] - 1 and trans_y > f2.shape[1] - 1):
# continue
# divided by two parts with integer & decimal number
tx = int(trans_x) -col_min
ty = int(trans_y) -row_min
a = trans_x - tx
b = trans_y - ty
if tx<canvas.shape[1] and ty<canvas.shape[0] and tx>0 and ty>0:
canvas[ty,tx]=im1_interpolate[y,x]
# Bilinear Interpolation
# if ty+1<im1.shape[0] and tx+1<im1.shape[1]:
# canvas1[ty][tx] = ((((1.0 - a) * (1.0 - b)) * im1[ty,tx])
# + ((a * (1.0 - b)) * im1[ty,tx + 1])
# + ((a * b) * im1[ty + 1,tx + 1])
# + (((1.0 - a) * b) * im1[ty + 1,tx]))
# Image stitch
# M, N = f1.shape[:2]
# f_stitched = np.copy(warped)
#f_stitched[0:M, 0:N, :] = f1
# Plot
# plt.subplot(221)
# plt.imshow(f1)
# plt.axis('off')
# coordinates_2=np.array(coordinates_2)
# coordinates_1=np.array(coordinates_1)
# plt.scatter(coordinates_2[:, 0], coordinates_2[:, 1], marker='x')
# plt.subplot(222)
# plt.imshow(f2)
# plt.axis('off')
# plt.scatter(coordinates_1[:, 0], coordinates_1[:, 1], marker='x')
# plt.subplot(223)
plt.imshow(canvas)
plt.axis('off')
#plt.subplot(224)
#plt.imshow(f_stitched)
#plt.axis('off')
plt.show()
Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).
Stitching image 2 to 3 using H23
for y in range(0, h2):
for x in range(0, w2):
pixel = np.array([x,
y,
1])
# Resource_pixel = np.asarray(np.asmatrix(inv_my_homo) * np.asmatrix(pixel))
#Resource_pixel = np.asarray(np.asmatrix(My_Homography_arr) * np.asmatrix(pixel))
Resource_pixel = np.asarray(H23* np.asmatrix(pixel).T)
# Coordinate scale
trans_x = Resource_pixel[0][0] / Resource_pixel[2][0]
trans_y = Resource_pixel[1][0] / Resource_pixel[2][0]
# Continue that pixels not matched
# if (trans_x < 0 or trans_y < 0
# or trans_x > f2.shape[0] - 1 or trans_y > f2.shape[1] - 1):
# # if (trans_x < 0 and trans_y < 0
# # and trans_x > f2.shape[0] - 1 and trans_y > f2.shape[1] - 1):
# continue
# divided by two parts with integer & decimal number
tx = int(trans_x) -col_min
ty = int(trans_y) -row_min
a = trans_x - tx
b = trans_y - ty
if tx<canvas.shape[1] and ty<canvas.shape[0] and tx>0 and ty>0:
canvas[ty,tx]=im2_interpolate[y,x]
# Bilinear Interpolation
# if ty+1<im1.shape[0] and tx+1<im1.shape[1]:
# canvas1[ty][tx] = ((((1.0 - a) * (1.0 - b)) * im1[ty,tx])
# + ((a * (1.0 - b)) * im1[ty,tx + 1])
# + ((a * b) * im1[ty + 1,tx + 1])
# + (((1.0 - a) * b) * im1[ty + 1,tx]))
# Image stitch
# M, N = f1.shape[:2]
# f_stitched = np.copy(warped)
#f_stitched[0:M, 0:N, :] = f1
# Plot
# plt.subplot(221)
# plt.imshow(f1)
# plt.axis('off')
# coordinates_2=np.array(coordinates_2)
# coordinates_1=np.array(coordinates_1)
# plt.scatter(coordinates_2[:, 0], coordinates_2[:, 1], marker='x')
# plt.subplot(222)
# plt.imshow(f2)
# plt.axis('off')
# plt.scatter(coordinates_1[:, 0], coordinates_1[:, 1], marker='x')
# plt.subplot(223)
plt.imshow(canvas)
plt.axis('off')
#plt.subplot(224)
#plt.imshow(f_stitched)
#plt.axis('off')
plt.show()
Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).
Stitching image 4 to canvas using H43:
for y in range(0, h4):
for x in range(0, w4):
pixel = np.array([x,
y,
1])
# Resource_pixel = np.asarray(np.asmatrix(inv_my_homo) * np.asmatrix(pixel))
#Resource_pixel = np.asarray(np.asmatrix(My_Homography_arr) * np.asmatrix(pixel))
Resource_pixel = np.asarray(H43* np.asmatrix(pixel).T)
# Coordinate scale
trans_x = Resource_pixel[0][0] / Resource_pixel[2][0]
trans_y = Resource_pixel[1][0] / Resource_pixel[2][0]
# Continue that pixels not matched
# if (trans_x < 0 or trans_y < 0
# or trans_x > f2.shape[0] - 1 or trans_y > f2.shape[1] - 1):
# # if (trans_x < 0 and trans_y < 0
# # and trans_x > f2.shape[0] - 1 and trans_y > f2.shape[1] - 1):
# continue
# divided by two parts with integer & decimal number
tx = int(trans_x) -col_min
ty = int(trans_y) -row_min
a = trans_x - tx
b = trans_y - ty
if tx<canvas.shape[1] and ty<canvas.shape[0] and tx>0 and ty>0:
canvas[ty,tx]=im4_interpolate[y,x]
# Bilinear Interpolation
# if ty+1<im1.shape[0] and tx+1<im1.shape[1]:
# canvas1[ty][tx] = ((((1.0 - a) * (1.0 - b)) * im1[ty,tx])
# + ((a * (1.0 - b)) * im1[ty,tx + 1])
# + ((a * b) * im1[ty + 1,tx + 1])
# + (((1.0 - a) * b) * im1[ty + 1,tx]))
# Image stitch
# M, N = f1.shape[:2]
# f_stitched = np.copy(warped)
#f_stitched[0:M, 0:N, :] = f1
# Plot
# plt.subplot(221)
# plt.imshow(f1)
# plt.axis('off')
# coordinates_2=np.array(coordinates_2)
# coordinates_1=np.array(coordinates_1)
# plt.scatter(coordinates_2[:, 0], coordinates_2[:, 1], marker='x')
# plt.subplot(222)
# plt.imshow(f2)
# plt.axis('off')
# plt.scatter(coordinates_1[:, 0], coordinates_1[:, 1], marker='x')
# plt.subplot(223)
plt.imshow(canvas)
plt.axis('off')
#plt.subplot(224)
#plt.imshow(f_stitched)
#plt.axis('off')
plt.show()
Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).
Stitching image 5 to canvas using H53 homography matrix:
for y in range(0, h5):
for x in range(0, w5):
pixel = np.array([x,
y,
1])
# Resource_pixel = np.asarray(np.asmatrix(inv_my_homo) * np.asmatrix(pixel))
#Resource_pixel = np.asarray(np.asmatrix(My_Homography_arr) * np.asmatrix(pixel))
Resource_pixel = np.asarray(H53* np.asmatrix(pixel).T)
# Coordinate scale
trans_x = Resource_pixel[0][0] / Resource_pixel[2][0]
trans_y = Resource_pixel[1][0] / Resource_pixel[2][0]
# Continue that pixels not matched
# if (trans_x < 0 or trans_y < 0
# or trans_x > f2.shape[0] - 1 or trans_y > f2.shape[1] - 1):
# # if (trans_x < 0 and trans_y < 0
# # and trans_x > f2.shape[0] - 1 and trans_y > f2.shape[1] - 1):
# continue
# divided by two parts with integer & decimal number
tx = int(trans_x) -col_min
ty = int(trans_y) -row_min
a = trans_x - tx
b = trans_y - ty
if tx<canvas.shape[1] and ty<canvas.shape[0] and tx>0 and ty>0:
canvas[ty,tx]=im5_interpolate[y,x]
# Bilinear Interpolation
# if ty+1<im1.shape[0] and tx+1<im1.shape[1]:
# canvas1[ty][tx] = ((((1.0 - a) * (1.0 - b)) * im1[ty,tx])
# + ((a * (1.0 - b)) * im1[ty,tx + 1])
# + ((a * b) * im1[ty + 1,tx + 1])
# + (((1.0 - a) * b) * im1[ty + 1,tx]))
# Image stitch
# M, N = f1.shape[:2]
# f_stitched = np.copy(warped)
#f_stitched[0:M, 0:N, :] = f1
# Plot
# plt.subplot(221)
# plt.imshow(f1)
# plt.axis('off')
# coordinates_2=np.array(coordinates_2)
# coordinates_1=np.array(coordinates_1)
# plt.scatter(coordinates_2[:, 0], coordinates_2[:, 1], marker='x')
# plt.subplot(222)
# plt.imshow(f2)
# plt.axis('off')
# plt.scatter(coordinates_1[:, 0], coordinates_1[:, 1], marker='x')
# plt.subplot(223)
plt.imshow(canvas)
plt.axis('off')
#plt.subplot(224)
#plt.imshow(f_stitched)
#plt.axis('off')
plt.show()
Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).
Plotting Canvas containing all images stitched together:
plt.imshow(canvas/255)
<matplotlib.image.AxesImage at 0x2264168d340>